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Can someone explain to me why the x-axis of symmetry is always -b/2a : r/askmath

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Can someone explain to me why the x-axis of symmetry is always -b/2a : r/askmath

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I tried graphing my textbook examples of polar curves in cartesian form on desmos, but they're not matching up. did i do something wrong? green is my attempt at a cardioid, black is my attempt at a “flower”. : r/askmath